We give a simple proof, via query elimination, of a result due to O'Donnell, Saks, Schramm, and Servedio, which shows a lower bound on the zero-error
expected query complexity of a function $f$ in terms of the maximum
influence of any variable of $f$. Our lower bound also applies to
the two-sided error expected query complexity of $f$, and it allows
an immediate extension which can be used to prove stronger lower
bounds for some functions.